Laws of Pendulum Motion

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Pendulums have interesting properties that physicists use to describe other objects. For example, planetary orbit follows a similar pattern. These properties come from a series of laws that govern the pendulum’s movement. By learning these laws, you can begin to understand some of the basic tenets of physics and of motion in general.

Pendulum Terminology

The laws of pendulum motion govern the timing in clocks.
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You can make a pendulum from almost anything. Imagine a ball attached to the end of a string: this makes a pendulum. Physicists typically refer to the ball as the “pendulum bob.” Pendulum movement swings in an angle from side to side; imagine the hanging pendulum of a clock. Physicists refer to the motion of pendulums in oscillations. One oscillation describes the full movement from one point and back. Picture lifting the pendulum as high as possible to the right side; one oscillation would go from that point all the way to the left side and back.


The physics of pendulum motion led to an important result in physics.
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The Laws that govern pendulum motion led to the discovery of an important property. Physicists break up forces into a vertical and a horizontal component. In pendulum motion, three forces work directly on the pendulum: the mass of the bob, gravity and the tension in the string. Mass and gravity both work vertically downward. Since the pendulum doesn’t move up or down, the vertical component of the string tension cancels out the mass and gravity. This shows that the mass of a pendulum has no relevance to its motion, but the horizontal string tension does.

Newton’s First Law

Newton’s first law defines the velocity of objects in response to forces. The law states that if an object moves at a specific speed and in a straight line, it will continue to move at that speed and in a straight line, infinitely, as long as no other force acts on it. Imagine throwing a ball straight forward; the ball would go around the earth over and over if air resistance and gravity did not act on it. This law shows that since a pendulum moves side to side and not up and down it has no up and down forces acting on it.

Newton’s Third Law

Newton’s third law states that every action has a reaction of equal force. This law works with the first law showing that although the mass and gravity cancel out the vertical component of string tension vector, nothing cancels out the horizontal component. This law shows that the forces acting on a pendulum can cancel each other. Physicists use Newton's first and third laws to prove the horizontal string tension moves the pendulum without regard to mass or gravity.

Period Law

Mathematicians use oscillating curves to describe pendulum motion.
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The period of a pendulum describes the length of time it takes a pendulum to go from one point, through one oscillation, and back. Because the mass of a pendulum has no bearing on its motion, physicists have proven that all pendulums have the same period for oscillation angles -- the angle between the center of the pendulum at its highest point and the center of pendulum at its stopped position -- less than 20 degrees.


About the Author

Josh Turner started writing in 2001. He wrote ad campaigns and business materials for Carpetland U.S.A. and his work has also appeared in his campus newspaper, “The Correspondent,” and “The Wellhouse” magazine. Turner is pursuing a Bachelor of Arts in mathematics with a minor in journalism from Indiana University.

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